# Probability and Random Processes

Spring 2022

Kannan Ramchandran

Lecture: TuTh 3:30-5 PM (Lewis 100)

Office Hours: Tu 5-6 PM (Cory 212)

## Announcements

- Welcome to EECS 126! Please read the course info and join Piazza.
- We will hold remote lecture/OH/discussion until 01/31 (subject to campus policy change). See calendar for the schedule and Piazza for Zoom links.

## Lecture Schedule

Schedule is subject to some changes.

Date | Topics | Readings |
---|---|---|

01/18 | Introduction, Probability Spaces, Conditional Probability, Law of Total Probability | B-T 1 |

01/20 | Independence, Bayes Rule, Discrete Random Variables | B-T 1, 2 |

01/25 | Expectation, Uniform, Geometric, Binomial and Poisson Distributions | B-T 2 |

01/27 | (Co)variance, Correlation, Conditional / Iterated Expectation, Law of Total Variance | B-T 2 |

02/01 | Continuous Probability, Uniform, Exponential Distributions | B-T 3 |

02/03 | Gaussian Distribution, Derived Distributions, Continuous Bayes | B-T 3, 4.1-4.2 |

02/08 | Order Statistics, Convolution, Moment Generating Functions | B-T 4.3-4.6 |

02/10 | MGFs, Bounds/Concentration Inequalities (Markov, Chebyshev, Chernoff) | B-T 5.1 |

02/15 | Convergence, Weak and Strong Law of Large Numbers, Central Limit Theorem | B-T 5.2-5.6, W 2.1-2.3 Convergence |

02/17 | Information Theory | Information Theory |

02/22 | No Lecture (Midterm) | |

02/24 | Binary Erasure Channel Capacity | W 1, 13.3, B-T 7.1-7.4 Capacity |

03/01 | Information Theory Wrapup | |

03/03 | Discrete Time Markov Chains, Stationary Distribution, Hitting Time, First Step Equations | W 1, 2.4, 2.6, 13.3, B-T 7.1-7.4 Markov Chains |

03/08 | DTMCs: Reversibility, Infinite States, Classification, Big Theorem | Reversibility |

03/10 | DTMC Wrapup | |

03/15 | Poisson Processes: Counting Process, Memorylessness, Merging, Splitting | B-T 6.1-6.3, W 13.4 |

03/17 | PP: Erlang Distribution, Random Incidence | B-T 6.1-6.3, W 13.4 |

03/29 | Continuous Time Markov Chains: Rate Matrix and Stationary Distribution | B-T 7.5, W 13.5 |

03/31 | CTMCs: Big Theorem, First Step Equations and Jump Chain | B-T 7.5, W 13.5 CTMCS |

04/05 | No Lecture (Midterm) | |

04/07 | Erdos-Renyi Random Graphs | Random Graphs |

04/12 | Maximum Likelihood Estimation, Maximum a Posteriori Estimation | B-T 8.1-8.2, 9.1, W 5.1 |

04/14 | Statistical Hypothesis Testing, Neyman-Pearson Lemma | Hypothesis Testing B-T 9.3-9.4, W 5.5-5.6, 6.5 |

04/19 | Minimum Mean Square Error Estimation, Vector Space of Random Variables | Hilbert space of RVs B-T 8.3-8.5, W 7.1-7.5 |

04/21 | Linear Least Square Estimate | W 7.1-7.5, W 8.1 |

04/26 | Jointly Gaussian Random Variables | Jointly Gaussian RVs W 6.3-6.4, 7.6, 8.1-8.3 |

04/28 | Orthogonal Updates and Kalman Filter | Kalman Filter (1) Kalman Filter (2) W 7.6, 8.1-8.3 |